8 Conclusions

The study of fundamental constants has witnessed tremendous progresses in the past years. In a decade, the constraints on their possible space and time variations have flourished. They have reached higher precision and new systems, involving different combinations of constants and located at different redshifts, have been considered. This has improved our knowledge on the equivalence principle and allowed to test it on astrophysical and cosmological scales. We have reviewed them in Section 3 and Section 4. We have emphasized the experimental observational progresses expected in the coming years such as the E-ELT, radio observations, atomic clocks in space, or the use of gravitational waves.

From a theoretical point of view, we have described in Section 5 the high-energy models that predict such variation, as well as the link with the origin of the acceleration of the universe. In all these cases, a spacetime varying fundamental constant reflects the existence of an almost massless field that couples to matter. This will be at the origin of a violation of the universality of free fall and thus of utmost importance for our understanding of gravity and of the domain of validity of general relativity. Huge progress has been made in the understanding of the coupled variation of different constants. While more model-dependent, this allows one to set stronger constraints and eventually to open an observational window on unification mechanisms.

To finish, we have discussed in Section 7 the ideas that try to understand the value of the fundamental constant. While considered as borderline with respect to the standard physical approach, it reveals the necessity of considering a universe larger than our own, and called the multiverse. It will also give us a hint on our location in this structure in the sense that the anthropic principle limits the Copernican principle at the basis of most cosmological models. We have stressed the limitations of this approach and the ongoing debate on the possibility to make it predictive.

To conclude, the puzzle about the large numbers pointed out by Dirac has led to a better understanding of the fundamental constants and of their roles in the laws of physics. They are now part of the general tests of general relativity, as well as a breadcrumbs to understand the origin of the acceleration of the universe and to more speculative structures, such as a multiverse structure, and possibly a window on string theory.

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